calc 3 - summer 2019

Brian Abbott, May 24, 2019

resources to go along with online calc 3 course using openstax and apex calculus as primary texts.

Table of Contents

  1. Unit 1: Vectors and Vector-Valued Functions
    1. Vectors in Space - f(x,y) = 1/a(x^2+y^2)
    2. Cross Product: Demo
    3. calc 3 - openstax - ex 3.2
    4. calc 3 - openstax - parametric curves in space
    5. calc 3 - openstax - some helices
    6. calc 3 - openstax - derivatives of vector valued functions - tangent vector
    7. calc 3 - openstax - ex 3.7
    8. calc 3 - vector functions of constant length
    9. calc 3 - Tangent Velocity Vectors
    10. calc 3 - TNB Frame
    11. calc 3 - openstax - projectile motion ex. 3.16
  2. Unit 2: Differentiation of Functions of Several Variables
    1. Intro to Functions in Several Variables
    2. Domains of Functions in Two Variables
    3. Limits of Multivariable Functions
    4. Limits that Do Not Exist at Origin
    5. Level Curves (Braxton Carrigan)
    6. Level Curves
    7. Level Curves
    8. Directional Derivative
    9. Directional derivatives and Gradient
    10. calc 3 - constrained min max problem
    11. calc 3 - lagrange multiplier example 1
    12. calc 3 - level sets review example
    13. calc 3 - level sets review question part 2
  3. Unit 3: Multiple Integration
    1. Riemann Sums of a Double Integral
    2. Iterated Double Integrals
    3. Double Integrals
    4. Double integral over a rectangle
    5. Double Integral over Type I Region
    6. Double Integral on Rectangular Region
    7. General Region Double Integral
    8. double integration - polar coordinates - r dθ dr
    9. Triple Integrals - an example to start
    10. Triple Integral in rectangula…
    11. Triple Integral Cylindrical C…
    12. Triple Integral Spherical Coordinates
    13. Geometric interpretation of the Jacobian
    14. Jacobian Animation
    15. Jacobian Locus
  4. Unit 4: Vector Calculus
    1. Vector Fields
    2. Vector Fields in 2D
    3. Vector field 3D
    4. Vector fields 3D
    5. Line Integral Visualization
    6. Line Integral of a Scalar Function
    7. Line integrals: Arc length & Area of fence
    8. Parametric surfaces
    9. Parametric Surfaces
    10. Copy of Parametric surface

1.

Unit 1: Vectors and Vector-Valued Functions

  • 1. Vectors in Space - f(x,y) = 1/a(x^2+y^2)
  • 2. Cross Product: Demo
  • 3. calc 3 - openstax - ex 3.2
  • 4. calc 3 - openstax - parametric curves in space
  • 5. calc 3 - openstax - some helices
  • 6. calc 3 - openstax - derivatives of vector valued functions - tangent vector
  • 7. calc 3 - openstax - ex 3.7
  • 8. calc 3 - vector functions of constant length
  • 9. calc 3 - Tangent Velocity Vectors
  • 10. calc 3 - TNB Frame
  • 11. calc 3 - openstax - projectile motion ex. 3.16

1.1.

Vectors in Space - f(x,y) = 1/a(x^2+y^2)

– Brian Abbott

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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2.

Unit 2: Differentiation of Functions of Several Variables

  • 1. Intro to Functions in Several Variables
  • 2. Domains of Functions in Two Variables
  • 3. Limits of Multivariable Functions
  • 4. Limits that Do Not Exist at Origin
  • 5. Level Curves (Braxton Carrigan)
  • 6. Level Curves
  • 7. Level Curves
  • 8. Directional Derivative
  • 9. Directional derivatives and Gradient
  • 10. calc 3 - constrained min max problem
  • 11. calc 3 - lagrange multiplier example 1
  • 12. calc 3 - level sets review example
  • 13. calc 3 - level sets review question part 2

2.1.

Intro to Functions in Several Variables

– Brian Abbott

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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3.

Unit 3: Multiple Integration

  • 1. Riemann Sums of a Double Integral
  • 2. Iterated Double Integrals
  • 3. Double Integrals
  • 4. Double integral over a rectangle
  • 5. Double Integral over Type I Region
  • 6. Double Integral on Rectangular Region
  • 7. General Region Double Integral
  • 8. double integration - polar coordinates - r dθ dr
  • 9. Triple Integrals - an example to start
  • 10. Triple Integral in rectangula…
  • 11. Triple Integral Cylindrical C…
  • 12. Triple Integral Spherical Coordinates
  • 13. Geometric interpretation of the Jacobian
  • 14. Jacobian Animation
  • 15. Jacobian Locus

3.1.

Riemann Sums of a Double Integral

– Brian Abbott, Greg Petrics

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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3.14.

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3.15.

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4.

Unit 4: Vector Calculus

  • 1. Vector Fields
  • 2. Vector Fields in 2D
  • 3. Vector field 3D
  • 4. Vector fields 3D
  • 5. Line Integral Visualization
  • 6. Line Integral of a Scalar Function
  • 7. Line integrals: Arc length & Area of fence
  • 8. Parametric surfaces
  • 9. Parametric Surfaces
  • 10. Copy of Parametric surface

4.1.

Vector Fields

Change the components of the vector field.
This applet was done thanks to the work of Linda Fahlberg-Stojanovska: [url=https://www.geogebra.org/u/lfs-d]https://www.geogebra.org/u/lfs-d[/url]
– Juan Carlos Ponce Campuzano

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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